Although visual representations are generally beneficial for learners, past research also suggests that often only a subset of learners benefits from visual representations. In this work, we designed and evaluated anticipatory diagrammatic self- explanation, a novel form of instructional scaffolding in which visual representations are used to guide learners' inference generation as they solve algebra problems in an Intelligent Tutoring System. We conducted a classroom experiment with 84 students in grades 5-8 in the US to investigate the effectiveness of anticipatory diagrammatic self-explanation on algebra performance and learning. The results show that anticipatory diagrammatic self-explanation benefits learners on problem-solving performance and the acquisition of formal problem-solving strategies. These effects mostly did not depend on students' prior knowledge. We analyze and discuss how performance with the visual representation may have influenced the enhanced problem-solving performance. [This paper was published in: "Proceedings of the Annual Meeting of the Cognitive Science Society," UC Merced, 2021, pp. 1858-1864.]